Question

centimeters and 10 centimeters. (Assume mass is a constant.) cm2/sec . Find dw/dt using the appropriate Chain Rule.​ Function w=xsiny x=eᵗ,y=π−t dw/dt= sin(y)(eᵗ)+xcos(y)(−1) ​ Value t=0​ Evaluate dw/dt at the given value of t.

Answer 1

To find dw/dt using the Chain Rule, we need to take the derivative of w with respect to x and multiply it by the derivative of x with respect to t. The resulting expression is -x * sin(t) * e^t.

Step-by-step explanation:

To find dw/dt using the Chain Rule, we need to take the derivative of w with respect to x and multiply it by the derivative of x with respect to t. Let's start by finding the derivative of w with respect to x.

w = x * sin(y) = x * sin( - t) = x * sin * cos(t) - x * cos * sin(t) = -x * sin(t)

Now, let's find the derivative of x with respect to t. x = e^t, so dx/dt = e^t.

Finally, we can find dw/dt using the Chain Rule: dw/dt = dw/dx * dx/dt = (-x * sin(t)) * e^t = -x * sin(t) * e^t.